Download Biconditional

Geometry:
2.3: Biconditionals and Definitions
Define:
Biconditional:
_____________________________________________________________
1) Writing a Biconditional:
Statement: If the sum of the measures of two angles is 180, then the two
angles are supplementary.
Converse:
___________________________________________________________
Is the converse true or false? _________
Biconditional:
_______________________________________________________
You try:
Statement: If two angles have equal measure, then the angles are
congruent.
Converse:
___________________________________________________________
Is the converse true or false? _________
Biconditional:
_______________________________________________________
2) Identifying the conditionals in a biconditional:
What are the two statements that form this biconditional?
A ray is an angle bisector, if and only if it divides an angle into two
congruent angles.
p: _____________________________________________________________
q: _____________________________________________________________
𝑝⟶𝑞:
_____________________________________________________________
𝑞 ⟶ 𝑝:
_____________________________________________________________
You Try:
What are the two conditionals that form this biconditional?
Two numbers are reciprocals if and only if their product is 1
p: _____________________________________________________________
q: _____________________________________________________________
𝑝⟶𝑞:
_____________________________________________________________
𝑞 ⟶ 𝑝:
_____________________________________________________________
True biconditionals serve as effective definitions.
Here are the qualities that make for a good definition:
 A good definition ___________________________________. These
terms should be commonly understood or already defined.
 A good definition is_____________________. Good definitions avoid
words such as large, sort of, and almost.
 A good definition is ____________________. That means you can
write a good definition as a true biconditional.
3) Writing a Definition as a Biconditional:
Is this definition of a quadrilateral reversible? If yes, write as a true
biconditional.
Definition: A quadrilateral is a polygon with 4 sides.
Conditional:____________________________________________________
_______________________________________________________________
________________________
Converse:______________________________________________________
_______________________________________________________________
_________________________
Biconditional:
___________________________________________________________
You Try:
Is this definition of a quadrilateral reversible? If yes, write it as a true
biconditional.
Definition: A straight angle is an angle that measures 180o.
Conditional:____________________________________________________
_______________________________________________________________
________________________
Converse:______________________________________________________
_______________________________________________________________
_________________________
Biconditional:
___________________________________________________________
4) Identifying a Good Definition
Good definitions cannot be disproven by a counter example.
Evaluate the definitions below:
A. A fish is an animal that swims
B. Rectangles have 4 corners.
C. Giraffes are animals with very long necks.
D. A penny is a coin worth one cent.
You try:
Is the following statement a good definition? Explain.
A square is a figure with four right angles.